A double Metropolis–Hastings sampler for spatial models with intractable normalizing constants

The problem of simulating from distributions with intractable normalizing constants has received much attention in the recent literature. In this paper, we propose an asymptotic algorithm, the socalled double Metropolis-Hastings (MH) sampler, for tickling this problem. Unlike other auxiliary variable algorithms, the double MH sampler removes the need of exact sampling, the auxiliary variables being generated using MH kernels, and thus can be applied to a wide range of problems for which exact sampling is not available. While for the problems for which exact sampling is available, it can typically produce the same accurate results as the exchange algorithm, but using much less CPU time. The new method is illustrated by various spatial models.